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Solve for each variable: x ≈ , y ≈

Solve for each variable: x ≈ , y ≈

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve for each variable: x ≈ , y ≈ .

 

The image depicts a right triangle with one of its angles measuring 45 degrees. The side opposite the 45-degree angle is labeled \( y \), the side adjacent to the 45-degree angle is labeled 11, and the hypotenuse is labeled \( x \). **Key Features of the Triangle:** - **Right Triangle**: This triangle includes a right angle (90 degrees). - **One Known Angle**: One angle measures 45 degrees. - **Known Side**: The side opposite the right angle measures 11 units. **Identifying Sides:** - **Hypotenuse (\( x \))**: The side opposite the right angle, not labeled with a numerical value here. - **Opposite Side (\( y \))**: The side across from the 45-degree angle. - **Adjacent Side**: The side along the 11-unit length. Since this is a 45-45-90 triangle, properties specific to this triangle can be applied. In a 45-45-90 triangle, the legs are equal, and the hypotenuse is \(\sqrt{2}\) times longer than each leg. If further calculations are needed, trigonometric ratios or the Pythagorean theorem may be useful.
Transcribed Image Text:The image depicts a right triangle with one of its angles measuring 45 degrees. The side opposite the 45-degree angle is labeled \( y \), the side adjacent to the 45-degree angle is labeled 11, and the hypotenuse is labeled \( x \). **Key Features of the Triangle:** - **Right Triangle**: This triangle includes a right angle (90 degrees). - **One Known Angle**: One angle measures 45 degrees. - **Known Side**: The side opposite the right angle measures 11 units. **Identifying Sides:** - **Hypotenuse (\( x \))**: The side opposite the right angle, not labeled with a numerical value here. - **Opposite Side (\( y \))**: The side across from the 45-degree angle. - **Adjacent Side**: The side along the 11-unit length. Since this is a 45-45-90 triangle, properties specific to this triangle can be applied. In a 45-45-90 triangle, the legs are equal, and the hypotenuse is \(\sqrt{2}\) times longer than each leg. If further calculations are needed, trigonometric ratios or the Pythagorean theorem may be useful.
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